A Complete Decomposition of Stochastic Differential Equations
arXiv:2601.07834v11 citations
Originality Incremental advance
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This provides a foundational mathematical framework for analyzing and constructing stochastic processes, which is incremental but clarifies structural properties in stochastic calculus.
The authors tackled the problem of decomposing stochastic differential equations with given time-dependent marginal distributions, showing that any such equation can be uniquely decomposed into three specific matrix and scalar fields.
We show that any stochastic differential equation with prescribed time-dependent marginal distributions admits a decomposition into three components: a unique scalar field governing marginal evolution, a symmetric positive-semidefinite diffusion matrix field and a skew-symmetric matrix field.